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Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes
Author(s) -
GonzálezParra Gilberto,
Arenasm Abraham J.,
ChenCharpentier Benito M.
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21804
Subject(s) - mathematics , finite difference , observable , partial derivative , stability (learning theory) , finite difference method , derivative (finance) , finite difference scheme , nonlinear system , scheme (mathematics) , numerical analysis , mathematical analysis , computer science , physics , quantum mechanics , machine learning , financial economics , economics
In this article, we construct a numerical method based on a nonstandard finite difference scheme to solve numerically a nonarbitrage liquidity model with observable parameters for derivatives. This nonlinear model considers that the parameters involved are observable from order book data. The proposed numerical method use a exact difference scheme in the linear convection‐reaction term, and the spatial derivative is approximated using a nonstandard finite difference scheme. It is shown that the proposed numerical scheme preserves the positivity as well as stability and consistence. To illustrate the accuracy of the method, the numerical results are compared with those produced by other methods. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 210‐221, 2014